Local gravity field modeling based on satellite altimetry observations and Least Squares Collocation with improved covariance and patching approach in Oman Sea

Document Type : Research Article


Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran.


The Oman Sea is the meeting point of the Eurasian and Arabian tectonic plates, where the Makran subduction zone is located. Knowledge of the behavior and local changes of the gravity field is of great importance in the study and modeling of the complex tectonic structure in this area, which has been less addressed. In this research, SARAL/AltiKa satellite observations have been used, which has higher spatial resolution and, as a result, higher range precision due to the measurement in the Ka frequency band. The SARAL/AltiKa satellite altimetry data is used for the preliminary process. Then atmospheric delays, geophysical effects, cross-examination and mean dynamic topography model were corrected. After performing these corrections and reaching the geoid height in the study area, the EIGEN6C4 global model was used to remove the long wavelengths of the gravity field up to the degree and order 180 from the geoid height signal. As a result, the residual geoid height (∆N) are prepared as an input signal for the marine gravity modeling. On the other hand, in most of the other methods used in earth gravity field modeling, to simplify the calculations, two assumptions of stationarity and isotropy of the gravity field are taken into account, which means that the gravity function does not depend on the changes in the azimuth and the position of the observations. These assumptions are not always valid. In this research, in the first step the long-wavelength of input signal is removed. Then the process continued with residual geoid height. Next, the improved covariance approach is used to increase the accuracy of determining the covariance. Also the idea of patching is applied. Those three steps provide a solution to reduce the negative effects of the stationary assumption in the local modeling of gravity field. The results of this research in 234 ship borne gravimetric observations were evaluated. The improvement of quality of the covariance with the idea of patching and improved covariance approach enhanced the local modeling results of the gravity field. It was found that with patching, the field modeling accuracy was increased by 25.1% (1.04 mgal) with the Tscherning-Rapp 1974 approach and 11.6% (0.33 mgal) with the improved covariance approach. Similarly, the improved covariance approach also improved the local modeling of gravity field. Using this approach increases the accuracy of local modeling by 31.3% (1.27 mgal) without patching and by 18% (0.56 mgal) with patching. As a result, it was found that removing long-wavelength and using improved covariance and patching increases the accuracy of the local modeling of the gravity field with more than 39% (1.6 mgal) as compared to the Tscherning-Rapp 1974 covariance function without patching in the Oman Sea. Moreover, applying the mentioned approaches in region 1 with independent covariance shows 47% (2.25 mgal) increase in accuracy in the local modeling of the gravity field. This improvement is equivalent to 11.3%(0.33 mgal) higher accuracy than the available global gravity models.


Main Subjects

Andersen, O. (2013). Marine Gravity and Geoid from Satellite Altimetry, Geoid determination: theory and methods, Springer Science& Business Media. 9.
Foerste, CH. Bruinsma, S. L., Abrikosov, O., Lemoine, J. M., Marty, J. C., Flechtner, F., Balmino, G., Barthelmes, F., & Biancale, R. (2014). EIGEN-6C4 the latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services. 10.
Heydarizadeh Shali, H., Ramouz, S., Safari, A., & Barzaghi, R. (2020). Assessment of Tscherning-Rapp covariance in Earth gravity modeling using gravity gradient and GPS/leveling observations. EGU General Assembly Conference.
Kalnins, M. L. (2011). Spatial variations in the effective elastic thickness of the lithosphere and their tectonic implications. Oxford University.
Moritz, H. (1980). Advanced physical geodesy. Original from the University of Michigan. Wichmann.
Rummel, R., & Rapp, R. H. (1977). Undulation and anomaly estimation using GEOS-3 altimeter data without precise satellite orbits. Bulletin Geodesique. 1.51, 73-88.
Ramouz, S., Afrasteh, Y., Reguzzoni, M., & Safari, A. (2020). Assessment of local covariance estimation through Least Squares Collocation over Iran. Advances in Geosciences. 50, (65-75).
Sandwell, D. T., & Smith, W. H. F. (1997). Marine gravity anomaly from Geosat and ERS 1 satellite altimetry. Journal of Geophysical Research: Solid Earth, 102, 10039-10054.
Sansò, F. & Sideris, M. G. (2013). Geoid determination: theory and methods. Springer Science & Business Media.
Sandwell, D. T., Müller, D. R., Smith, W. H., Garcia, E., & Francis, R. (2014). New global marine gravity model from CryoSat-2 and Jason-1 reveals buried tectonic structure. Journal Science, 364(6205), 65-67.
Safari, A., Ramouz, S., & Jomegi, A. (2014). Verification of crust density effect on the gravity field modeling by least squares collocation. International Conference on Advanced Geophysics and Physics. Bangkok. Thailand.
Tscherning, C. C., & Rapp, R. H. (1974). Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models. Report Notes for Ohio State University of Columbus Department of Geodetic Science. Ohio.
Tscherning, C. C. (1994). Geoid determination by least-squares collocation using GRAVSOFT. Lecture Notes for the International School for the Determination and use of the Geoid. Milan.
Verron, J., Bonnefond, P., Anderson, O., Ardhuin, F., Berge-Nguyen, M., Bhowmik, S., Blumstein, D., Boy, F., Brodeau, L., Cretaux, J. F., Dabat, M. L., Dibarboure, G., Fleury, S., Garnier, F., Gourdeau, L., Marks, K., Queruel, N., Sandwell, D., Smith, W. H. F., & Zaron, E. D. (2020) The SARAL/AltiKa mission: A step forward to the feature of altimetry. Advances in Space Research.